Question

The disintegration rate of a certain radioactive sample at any instant is 4750 dpm (disintegration per minute). Five minutes later, the rate becomes 2700 dpm. Calculate half-life of sample.

• A. 6.1328 min
• B. 9.3328 min
• C. 7.2328 min
• D. None of these

Answer 1

The correct option is A 6.1328 min

$-\frac{dN}{dt}=\lambda N_0$ at start
$-\frac{dN}{dt}=\lambda N_0$ after time t
$4750=\lambda N_0$
$2700=\lambda N$
$\therefore \frac{N_0}{N}=\frac{4750}{2700}$
Also $\lambda =\frac{2.303}{5}log\frac{N_0}{N}$
$=\frac{2.303}{5}log\frac{4750}{200}=0.113mi{n}^{-1}$
$\therefore t_{50}=\frac{0.693}{\lambda }=\frac{0.693}{0.113}=6.1328min$